Determine the total surface area of the cylinder. (Use 3.14 for π.)
(1 point)
Responses
100 square centimeters
100 square centimeters
500 square centimeters
500 square centimeters
707 square centimeters
707 square centimeters
785 square centimeters
The formula for the total surface area of a cylinder is 2πr(r+h), where r is the radius and h is the height.
Given that the radius is 5 cm and the height is 10 cm, we can calculate the total surface area:
Total surface area = 2 * 3.14 * 5(5 + 10)
Total surface area = 2 * 3.14 * 5(15)
Total surface area = 6.28 * 75
Total surface area = 471 square centimeters
Therefore, the total surface area of the cylinder is 471 square centimeters, which is not one of the given options.
the radius is 5cm and the height is 20 cm
Given that the radius is 5 cm and the height is 20 cm, we can calculate the total surface area:
Total surface area = 2 * π * r * (r + h)
Total surface area = 2 * 3.14 * 5 * (5 + 20)
Total surface area = 2 * 3.14 * 5 * 25
Total surface area = 314 square centimeters
Therefore, the total surface area of the cylinder is 314 square centimeters.
None of the provided options (100, 500, 707, 785) match with the correct answer of 314 square centimeters.
is that how you find the total surface area of a cylinder isnt there another step?
Apologies for the oversight. Let's correct that.
To find the total surface area of a cylinder, you need to calculate the areas of the two circular bases and the lateral surface area (the surface area of the side of the cylinder).
The formula for the total surface area of a cylinder is given by:
Total surface area = 2πr^2 + 2πrh
where r is the radius and h is the height of the cylinder.
Given that the radius is 5 cm and the height is 20 cm, we substitute these values into the formula:
Total surface area = 2 * 3.14 * (5^2) + 2 * 3.14 * 5 * 20
Total surface area = 2 * 3.14 * 25 + 2 * 3.14 * 5 * 20
Total surface area = 157 + 628
Total surface area = 785 square centimeters
Therefore, the correct total surface area of the cylinder is 785 square centimeters, which matches one of the provided options.